J. Chem. Sci., Vol. 119, No. 2, March 2007, pp. 113–121. © Indian Academy of Sciences.
On the origin of the anomalous ultraslow solvation dynamics in
heterogeneous environments
KANKAN BHATTACHARYYA1, * and BIMAN BAGCHI2,*
1
Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur,
Kolkata 700 032
2
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012
e-mail: [email protected]; [email protected]
Abstract. Many recent experimental studies have reported a surprising ultraslow component (even
>10 ns) in the solvation dynamics of a polar probe in an organized assembly, the origin of which is not
understood at present. Here we propose two molecular mechanisms in explanation. The first one involves
the motion of the ‘buried water’ molecules (both translation and rotation), accompanied by cooperative
relaxation (‘local melting’) of several surfactant chains. An estimate of the time is obtained by using an
effective Rouse chain model of chain dynamics, coupled with a mean first passage time calculation. The
second explanation invokes self-diffusion of the (di)polar probe itself from a less polar to a more polar
region. This may also involve cooperative motion of the surfactant chains in the hydrophobic core, if the
probe has a sizeable distribution inside the core prior to excitation, or escape of the probe to the bulk
from the surface of the self-assembly. The second mechanism should result in the narrowing of the full
width of the emission spectrum with time, which has indeed been observed in recent experiments. It is
argued that both the mechanisms may give rise to an ultraslow time constant and may be applicable to
different experimental situations. The effectiveness of solvation as a dynamical probe in such complex
systems has been discussed.
Keywords. Ultraslow solvation dynamics; heterogeneous environments; polar probe.
1.
Introduction
Time-dependent Stokes shift of fluorescence from a
probe dye molecule has provided a wealth of information on the dynamics of dipolar liquids.1–11 In
these experiments, a sudden (instantaneous) change
in the charge distribution of the probe molecule is
created optically using an ultrashort laser pulse.
Subsequent change in the energy of the probe solute
is monitored through the fluorescence frequency of
the probe. Solvation time correlation function is defined
as1–3
S (t ) = (ν (t ) − ν (∞)) /(ν (0) − ν (∞)),
(1)
where ν(t) is the average frequency at a time t of the
fluorescence spectrum from the probe molecule. S(t)
evolves from unity at time t = 0 to zero as time goes
to infinity. The time dependence of S(t) provides detailed information of the time-dependent response of
the liquid to the sudden change in the charge distri*For correspondence
bution in the probe. Since energy derives contributions from interactions with many solvent molecules,
this response is collective. If the perturbation is
small, the dynamics described by S(t) is expected to
be equivalent to the decay of the equilibrium time
correlation function, C(t), which is given by
C (t ) = 〈δ Esolv (0)δ Esolv (t )〉 / 〈δ Esolv (0)δ Esolv (0)〉, (2)
where δEsolv(t) is the fluctuation in the solvation energy about the equilibrium solvation energy. Detailed knowledge of the time-dependence of C(t) is
of fundamental importance to understand the solvent
effects in many chemical processes, such as electron
transfer, dephasing.
The microscopic processes involved in the solvation
of a polar solute can be quite different in a heterogeneous environment. This is because in a heterogeneous environment, solvation energy of a polar probe
derives contribution from several different sources.
Thus, the solvation energy may be decomposed as
ΔE (t ) = ∑ ΔEi (t ) ,
(3)
i
113
114
Kankan Bhattacharyya and Biman Bagchi
where ΔEi denotes contribution of the ith component. The different contributions include interaction
of the polar probe with the surface charges (e.g.,
polar head groups), the interfacial and the bulk
water and the counterions. The relative amplitude of
the contribution may depend on the location of the
probe. An organized assembly is heterogeneous on a
length scale longer than a molecule. As a result, an
almost universal feature of solvation dynamics in a
organized assembly is the highly non-exponential
nature of the solvation energy relaxation. Thus,
time-dependent response of such a system may be
represented as
C (t ) = ∑ ai exp( −t / τ i ),
(4)
i
where τi is the time constant of the ith contribution.
Recently, there have been a large number of studies
on solvation dynamics in various media, ranging
from simple liquids (such as water, acetonitrile) to
complex systems (micelles, vesicles, proteins).
Among simple liquids, solvation dynamics studies in
liquid water have attracted special attention for the
ubiquitous role of water in biology.4–9 Solvation in
pure water shows ultrafast solvation, with the initial
component in the few tens of femtoseconds. In bulk
water, even the slowest component is only about
1 ps.4–9 However, in a restricted environment, the
long time part of solvation dynamics slows down
dramatically.8–23 At the surfaces of proteins, solvation dynamics displays a component which is slower
by one to two orders of magnitude with time constants
ranging from few tens to few hundreds of picoseconds.11–15 The ultraslow component in a cyclodextrin cavity is nearly 1000 times slower than that
in bulk water.16 This dramatic slowing down of solvation dynamics is attributed to the freezing of
translational (and rotational) motions of water molecules inside the cyclodextrin cavity.17 However, in
the case of solvation dynamics in DNA,18 aqueous
polymer solutions,19 micelles,20–24 reverse micelles25–28
and some more recent studies of protein solvation
dynamics, a definite ultraslow component even
greater than 1 ns (1000 ps) has been observed.
There is yet no satisfactory explanation of the origin
of this ultraslow component. The existence of such a
slow component is indeed surprising. We have earlier proposed a model involving dynamic equilibrium between free and bound water molecules in
the vicinity of a biological macromolecule.12 According to this model the slow component of relaxa-
tion depends on the binding energy, i.e. free energy
difference (ΔGbf0 ) between bound and free water. In
the limit of high binding energy (kfb >> kbf) the time
constant for the slowest component is given by
kslow ≈ kbf−1 ,
(5)
where kbf denotes bound-to-free interconversion.
According to this model, the activation energy for
bound-to-free interconversion is ΔGbf0 + ΔG≠ where
ΔG≠ is the activation energy for free–bound interconversion.12 The dynamic exchange model is vindicated by a recent computer simulation22 and
experimental determination of activation energy in
solvation dynamics.23 According to the computer
simulation the hydrogen bond energy of the interfacial water molecules and the polar head groups is
stronger by 7–8 kcal mol–1 compared to bulk
water.23 From temperature variation of solvation
dynamics in a triton X-100 (TX) micelle has been
found to involve an activation energy of 9 kcal mol–1
and a positive entropy of activation.23 However, although, the dynamic exchange model is adequate to
explain the slow component in 30–500 ps time scale,
it cannot satisfactorily explain the ultraslow component. The reason may be that this model completely
ignores the role of motion of the macromolecular
chains and diffusion of the probe itself in a heterogeneous environment.
It may be noted that the translational diffusion of
the water molecules in many organized assemblies
has been studied MD simulations.29–32 According to
these simulations, the translational diffusion coefficients of water in the immediate neighbourhood of a
protein,29,30 micelle,22,23 and lipid membrane31,32 and
is 2–6 times slower than that in the bulk water.
However, the above estimate is only an average
which is dominated by fast-moving molecules and
does not provide a correct picture of the slow dynamics of water at the surface. Translational diffusion
deep inside the hydration layer of such a system may
be many times slower.
In this work, we consider the role of chain dynamics
and self-diffusion of probe in explaining the ultraslow component of solvation dynamics in an organized assembly.
2.
Theoretical formulation
Before we discuss the theoretical models we should
emphasize that an organized assembly is heterogeneous on a mesoscopic length scale, that is in the
Anomalous ultraslow solvation dynamics in heterogeneous environments
scale of 30–100 Å. The equilibrium solvation energy
of the charged probe is different in different phases
because the polarity and the effective dielectric constant of the individual phases are different. For example, the solvation energy of a polar probe inside
the hydrocarbon core of a micelle is expected to be
much less than that at the micelle-water interface
while the latter is again smaller than that in the bulk
water. For simplicity, we consider a two phase system,
with water being the outer phase. We also assume
that the probe is hydrophobic in its ground state.
Therefore, it is distributed primarily in the interface
and also inside the hydrophobic core. The excited state
of the probe, however, is polar (dipolar or charged).
The structure of the hydration shell of many other
macromolecules have been studied by computer
simulations22,24,27,31 and neutron scattering.35 The
simulations indicate that in the hydration layer the
macromolecules or surfactants are connected by hydrogen bond bridges involving water molecules
(water bridges). The exact number of water molecules and water bridges vary from one surfactant to
another. A single water molecule may form an intramolecular hydrogen bond bridge between two
oxygen atoms of the same surfactant chain or an intermolecular hydrogen bond bridge between two
neighbouring surfactant molecules. Tasaki33 identified two kinds of water bridges-one between two
oxygen atoms of the same chain and another between an oxygen atom of the chain and the oxygen
atom of another water molecule. Bandyopadhyay et
al34 reported one hydrogen atom forms a hydrogen
bond bridge between the two oxygen atoms of the
same chain of a surfactant. In the case of a lipid
(DMPC) bilayer about 70% of the surfactant
(DMPC) molecules are found to be linked by either
single or multiple intermolecular water bridges.31 In
many cases, two DMPC molecules are simultaneously
linked by 2, 3 and in rare cases by 4 parallel water
bridges.31 Such double or multiple hydrogen bonding gives certain amount of stability to these water
molecules. Also the clustering of the water molecules around a macromolecule leads to close packing and a density higher (1⋅25 times) than that in
bulk water.29
2.1 Model 1: Dynamics of surfactant chains with
buried, slow water
In this section, we consider the response of the buried
water following creation of the dipole in terms of
115
cooperative chain melting. Subsequent to the creation
of the polarization field by the external probe near
the surface, the buried water molecules inside a
micelle (or in general in an organized assembly)
would need to reorient to minimize their energy.
However, reorientation would require breaking of
hydrogen bond of a water molecule with another water molecule or with the surfactant and reformation
of hydrogen bond with the dipole created (figure 1).
This involves not only breaking and formation of
hydrogen bonds but also rotation and migration of
water molecules inside the layer and also of ‘breathing’ motion of the surfactant chains (figure 1).
Dynamics of such a processes is expected to be
rather slow and should be related to the dynamics of
the surfactant chain.
In order to estimate the relaxation of the buried
water molecules we assume the following simple
model. We assume that the water molecules need to
undergo a reaction between two minima which involves an activation barrier of ~9 kcal/mole and a
positive entropy factor.23 This activation energy is
not fully known but can be guessed with reasonable
accuracy. Next, we assume that the breakage of the
hydrogen bond and its realignment or relocation requires cooperative motion of the nearest neighbour
surfactant chains, may be two in number or greater.
Thus, what we propose is a local melting in the hydrophobic core (figure 1). In the following we present a quantitative estimate of the time required for
such melting. Note that this will be a slow process
and is expected to be the rate limiting step in the
solvation energy relaxation in the hydration shell.
In order for a cooperative melting to occur, one
requires phase coherence in the motion of all the
neighbouring chains. We model this by assuming
that each monomer of the chain has locally z number
of states (chain conformations). Next, one needs to
estimate the size of the region that can melt cooperatively. Let us assume that this number be denoted by
N. If τ0 is the time required for transition from the
ground to the excited state, then the time required
for the phase coherence required for local melting is
τ = z Nτ 0 .
(6)
For convenience we shall assume that z = 2, with a
ground state denoted by ‘0’ and the excited state by
‘1’. If we assume that the fluorescent solvation
probe is surrounded by two surfactant chains, then
the lowest size that can melt is a cell which contains
6 monomers, that is N = 2. Note that this is the lowest
116
Kankan Bhattacharyya and Biman Bagchi
Figure 1. A schematic illustration of the role of buried water in the solvation dynamics of a
probe which is initially located inside the self-assembly. This particular example illustrates the
possible rearrangement of water molecules in a micelle of surfactant of polyethylene glycol (polyoxyethylene surfactant),34 subsequent to optical excitation.
size and this can only be larger because of the involvement of more than 2 chains. It is difficult to
obtain an estimate of τ0 from any microscopic considerations because of the complexity of interactions
and the highly condensed state of the hydration
layer. We thus take recourse to the Rouse chain dynamics10 and assume that it can provide the estimate
via the largest wave number fluctuation relaxation
time.
τ 0 = 1/ λN −1 = (3D0 ) −1[ Nb /( N − 1)π ]2 .
(7)
For TX-100, N ≈ 10. We next need an estimate of D0
which we obtain by using Stokes–Einstein relation
(D0 = kT/6πηeffr) with effective viscosity of the
hydration layer, ηeff and radius r of the monomer
(C2H4O, in the case of the triton X-100 micelle) unit.
The logic of the above analysis is that breaking of
the hydrogen bond requires local excitation of the
nearby surfactants. This excitation we calculate by
using the normal modes of the surfactant chains and
a first passage time calculation. We assume that
these normal modes remain unperturbed by the presence of the others.
The advantage of the above simple expressions is
that we can now easily estimate the relaxation time.
If we assume that the radius of the monomer for a
TX micelle (C2H4O) unit is 3 Å and the effective
viscosity 0⋅3 cP,36 then the above expression gives a
value of τ0 ≈ 0⋅5 ns. Use of this time constant in (6)
gives a value of about 2 ns for the formation of the
local excited state. So, this is the approximate theoretical estimate of the ultraslow component arising
from the co-operative chain melting in the hydration
layer. Note that the time required for breaking of the
hydrogen bond is much smaller. It is about 10–
100 ps for a single hydrogen bond and somewhat
longer for the double bond which needs to be broken
consecutively and which can be further slowed
down by reformation.
The above estimate is certainly approximate and
depends on the parameters chosen. Still we believe
that we have obtained a reasonable number for the
rate constant of this complex process of cooperative
melting. The main features of this mechanism can be
summarized as the lengthening of time of relaxation
of deeply buried water in an organized assembly
(such as a triton X-100 micelles) due to high degree
of cooperatively required for these water molecules
to participate in the solvation dynamics.
2.2 Model 2: Self-diffusion of the probe
The second explanation invokes the motion of the
probe itself. Inside an organized assembly the local
polarity or the dielectric constant of confined water
Anomalous ultraslow solvation dynamics in heterogeneous environments
117
molecules varies strongly over distance from the
polar head groups. The large dielectric constant of
water arises largely from the self-polarization of
water molecules by neighbouring water molecules.37
In an organized assembly, the hydrogen-bond network of water is disrupted and water molecules become bound to the macromolecule by hydrogen
bond. As a result, the self-polarization of water
molecules is prevented. In principle, this effect is
minimized at large distances from the surfactant
and, hence, the local dielectric constant increases
with distance from the surfactant chain. The variation of the local dielectric constant in an inhomogeneous medium such as a vesicle gives rise to the rededge excitation shift (REES).38,39
An organized assembly usually consists of a large
hydrophobic core, and thus a fluorescent probe used
for solvation dynamics studies is largely hydrophobic in its ground state. In the model involving selfdiffusion we assume that in the ground state a significant percentage of the probe molecules are
trapped inside the relatively less polar region of the
micelles/reverse micelles with a major portion of the
probe inside the hydrocarbon chains. Subsequent to
the excitation, the dipole moment of the probe increases
substantially. Then the probe (which is initially in a
less polar region) diffuses to a more polar region.
Experimentally, self-diffusion manifests in narrowing of the emission spectrum with increase in
time (full width at half maxima, Γ). Recently, several
groups have reported decay of Γ with time (t).28,40
Qualitatively, this may explained as follows. At
t = 0, the probe molecules in different environments
are excited simultaneously. Due to the superposition
of the emission spectra in different environments at
short times, the spectral width of the emission spectrum is very large. Following electronic excitation
the probe molecule becomes highly polar and hence,
after excitation the probe molecules from all locations move towards the most polar region (figure 2).
After a sufficiently long time, all the probe molecules reach the most polar region and all of them
experience a more or less uniform environment.
This results in a small Γ. Thus the time constant of
decay of Γ may be ascribed to self-diffusion of the
probe.28,40 Hof et al40 reported that in lipid vesicles,
for some probes (9-AS, C17DiFu, laurdan) the
change in Γ is negligible while for some other
probes (e.g. prodan) there is an overall decrease by
20–25%. They, however, did not extract the time
constant of the decay of Γ(t) and did not discuss the
physical origin of this large decrease in Γ with time.
In figure 3 the decay reported by Hof et al40 is fitted
to bi-exponential with time constants 155 ps (20%)
and 1850 ps (80%), thus showing a time constant on
the nanosecond time scale. Dutta et al28 showed that
in a reverse micelle, Γ(t) of DCM exhibits a decrease by as much as 70%. They also showed that
the time constant of decay of Γ(t) of DCM is similar
to that of C(t) and hence, in this case the slow solva
Figure 2. A schematic illustration of probe motion subsequent to optical excitation of the probe to a more polar
state. A polar probe undergoes diffusion from a less polar
to a more polar region in an organized assembly. The
time dependence of the subsequent increase in the solvation stabilization energy is thus governed by probe diffusion in the confined system.
Figure 3. The time dependence of the full width at half
maxima, Γ, of the emission spectrum of prodan in a lipid
vesicle. The experimental results of Hof et al40 have been
fitted to a bi-exponential form with time constants 155 ps
(20%) and 1850 ps (80%), thus showing a time constant
in nanosecond time scale. The time dependence of Γ (t) is
due to the diffusion of the probe.
118
Kankan Bhattacharyya and Biman Bagchi
tion dynamics is attributed to self-diffusion of the
probe (DCM).28
It should be noted that a time-dependent change in
spectral width is observed only in selected cases.
For instance, the same probe (DCM) which exhibits
time-dependent change in Γ in a reverse micelle
does not show similar behaviour when entrapped in
a bile salt micelle.28 It is argued that in the latter
case the probe is confined in a very long (5 nm)
cylindrical water-filled core. As a result, within its
excited state lifetime, the probe does not come out in
bulk water and does not experience a large variation
of local polarity.
Note, that most dyes are distributed over both polar
and non-polar regions. If in the ground state a dye is
localized in the polar region, after excitation it does
not undergo self-diffusion and does not show a
nanosecond component. Only those dyes which are
initially in the non-polar region, migrate to a polar
region after excitation and hence, display an ultraslow component.
Several groups have analysed fluorescence anisotropy decays in an organized assembly in terms of the
‘wobbling-in-cone’ model to estimate the diffusion coefficient (D||) for translation parallel to the surface of
an organized assemble.41 It is observed that D|| is
smaller than that in bulk water (~10–5 cm2 s–1) only
by a factor of 2–5.41 Thus the probe undergoes diffusion over a distance (<z2> = 2D||t) of about 10 Å in
one ns. The diffusion from non-polar to polar region
may be in a direction normal to the surface of a micelle (or other organized assembly) and the corresponding diffusion coefficient D ⊥ may not be equal
to D||.
We now present a molecular theory for the above
dynamical process, namely, self-diffusion in an inhomogeneous medium A starting point for developing
such a molecular theory is to use a time-dependent
density functional (ρ) theory which gives the following expression for the position (X) dependent energy of interaction of a probe with the surrounding
medium
E ( X , t ) = ∫ dX ′CPSi ( X − X ′)δρ Si ( X ′, t )
− ∫ dX ′CPw ( X − X ′)δρ w ( X ′, t ),
(8)
where CPSi is the two particle direct correlation function between the polar probe and the ith group of the
surfactant/polymer and CPw is the probe-water direct
correlation function. In the inhomogeneous system,
these pair correlation functions themselves depend
on the location of the probe because density of surfactant or water is probe dependent. This makes a
quantitative evaluation of detailed dynamics a prohibitively difficult task. However, we can make some
progress because of the separation of time scales
among the processes that are involved. Since the diffusion of the probe is a slow process, we may approximate the solvation time correlation function by
〈 E (0) E (t )〉 = ∫ dxP ( x, t )〈 E ( x, 0) E ( E ( X , t )〉,
(9)
where P(X, t) gives the time evolution of the probe’s
location. A semi-quantitative description of the dynamics of the above process can be achieved by using
a Smoluchowski level description where the probability distribution of the solute probe may follow
the following equation of motion,
D ∂
∂P
∂2
( FP ),
=D 2 P−
k
∂t
∂X
B T ∂X
(10)
where the force F is due to the potential gradient felt
by the solute dipole created by the optical excitation.
This equation gives the time scale of the evolution
of the probability distribution under the force field.
The initial and the final distributions are obviously
different and are given by,
P0 ( X , t ) = n0 exp( − βV0 ( X )),
(11)
PEq ( X ) = n0 exp( − βVEq ( X )).
(12)
With (β = 1/kT), the initial and final potentials can
in principle be calculated from the density functional theory outlined above but that is still rather
hard. A simple way to express the potential V is to
invoke a continuum model with a space dependent
dielectric constant ε(X) (see figure 2). The potential
energy at a position X of an ionic probe can then be
crudely approximated by
V ( X ) = − q 2 / a[1 − 1/ ε ( X )].
(13)
The solvation dynamics probed is then determined
by the diffusion of the probe from the lower to the
larger dielectric constant. Inside the hydrophobic
core, the dielectric constant can be small, about 3–5,
while in the bulk, it is close to 80. The radius a is
Anomalous ultraslow solvation dynamics in heterogeneous environments
about 3–5 Å. The Smoluchowski equation can now
be solved to obtain the following expression
τ s ( X 0 , b) =
X
y
⎤
1⎡ M
⎢ ∫ dy exp( βV ( y )) ∫ dz exp( − βV ( z ) ⎥ .
D⎢X
⎥⎦
b
⎣ 0
(14)
where β = 1/kBT. X0 is the starting position, XM is the
final position and b is a position left of X0 where
probability is zero. Therefore, the average time is integration over the initial probability distribution,
P0(X). The position b could be taken as at 4–6 Å
inside the initial position of the probe inside the
micelle. D is an average diffusion constant which
should in principle also have an X dependence
which is neglected here for simplicity. Typically
viscosity in the core is expected to be about twice
that of liquid water.
If we assume that the probe is a sphere of radius
a = 3 Å, the partial charge created on the probe at
t = 0 is 0⋅5 esu, the probe diffuses as distance of 4a
with an average diffusion coefficient of 10–5 cm2/s,
then we obtain an estimate of 740 ps from the above
expressions. This is of course a crude estimate of the
time scale involved, meant to demonstrate that the
proposed mechanism can indeed give time constants
of the order observed in many experiments. The
main idea is that subsequent to excitation, the probe
may undergo a forced (or, biased) diffusion towards
more polar region, as illustrated in figure 2.
3.
Concluding remarks
The above analysis suggests that in some cases,
there could be more than one mechanism that can
give rise to an ultraslow component observed in recent experiments and the relative contributions can
be hard to estimate. One could, however, roughly
estimate the time scales responsible for the different
slow mechanisms. It is clear that the dynamic exchange between the free and the bound states of water molecules at the surface is important at relatively
short times. We expect this mechanism to be important up to about 500 ps or so and this model should
dominate in the 50–500 ps range. The case of TX100 is however, is extraordinary because here the
water molecules inside the hydration shell are highly
restricted and the dynamic exchange is expected to
be on the slow side. The self-diffusion of probe
should contribute next in order of time scale. As dis-
119
cussed, this should be in the 1–100 ns range, depending on the width of the hydrophobic core that the
probe needs to diffuse through. The role of the selfdiffusion of the probe could be estimated by the
variation of the width Γ at half-maximum of TRES.30,31
This could give an estimate of the relative importance of probe self-diffusion in the slow solvation.
There could be a third mechanism for ultraslow
solvation which involves the motion of the protein
or the self-assembly. At surfaces of proteins, the
solvation of a probe may derive contribution from
the motion of the protein side chains. Dielectric relaxation times in an aqueous solution a protein span
a wide range. The different components of dielectric
relaxation may classified as: (1) reorientation of
bulk water (8 ps); (2) overall tumbling or reorientation of the entire protein molecule (10–100 ns) and
(3) relaxation of water associated with the protein
(10–150 ps).9,12,42,43 According to the Stokes–Einstein
relation, the overall tumbling time (τm) of a biological system of volume V is given by,
τm = ηV/kBT,
(15)
where η is the viscosity of water. From this relation,
τm may be calculated if the volume of the macromolecule is known. For instance, the protein human
serum albumin (HSA) is an ellipsoidal of dimension
8 × 8× 3 nm. Thus for HSA τm is 25 ns in bulk
water. It should be emphasized that if the probe is
attached to the protein surface, the overall tumbling
gives rise to a relative motion of the probe and the
water molecules surrounding the protein.
Using the Stokes–Einstein relation, Wand et al45
calculated that for a protein of mass 50 kDa and
radius 26 A the overall tumbling time is 15 ns in
water, and that in the case of a reverse micelle, the
tumbling time (estimated for NMR relaxation)
decreases with viscosity of bulk hydrocarbon. The
dielectric relaxation of aqueous proteins exhibits a
10–100 ns component arising from tumbling of proteins.9 Thus one possible source of the very long
component (e.g. 10 ns reported for HSA) could be
tumbling of the protein.
One way to check the role of overall tumbling is
to create a situation when overall tumbling of the
protein is impossible. If a protein is confined inside
a water pool of the reverse micelle or a lipid, the
lipid vesicle or the reverse micelle tumbles as a
whole. The radius (rh) of a DMPC vesicle is about
15 nm.44 Thus, the volume of the vesicle is about
120
Kankan Bhattacharyya and Biman Bagchi
140 times than that of a single HSA molecule. From
(9), τm is 3500 ns for the lipid vesicle. Evidently,
overall tumbling of the lipid vesicle (τm = 3500 ns)
is impossible within the excited lifetime (1–2 ns) of
the fluorescent probe (DCM).
All the mechanisms discussed above provide explanations for the observed ultraslow time constant
in the solvation dynamics of an external probe in
self-assemblies. This also highlights the difficulty of
using solvation dynamics as a sensitive method to
study dynamics in such systems. One may need to
combine it with various other experimental techniques (such as REES, dielectric relaxation, NMR)
and also with computer simulations and theoretical
studies to gain an understanding of the relative role
of a specific mechanism in a given situation. However, slow dynamics can offer valuable insight into
the dynamics of the self-assembly itself.
Acknowledgement
This work was supported in part by grants from
the Department of Science and Technology and
the Council of Scientific and Industrial Research,
India.
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